The figure shows three ropes tied together in a knot. One of your friends pulls

Question

The figure shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force.
There is a 120 degree angle between the two ropes.
How hard must you pull on the third rope to keep the knot from moving?
In what direction must you pull on the third rope to keep the knot from moving?

I broke the two forces into vector components
Vector A is the one with a force of 3.0 units
Vector B is the one with a force of 5.0 units that is 120 degrees from vector A
Vector C is my unknown
Vector components are based on a coordinate system with vector A along the X axis
A= <3,0>
B= <2.5, 4.3>
C= ???
I have no clue what to do next after this.

Explanation / Answer

Hi, You did it correctly upto certain part. Vector A is resolved into the corresponding x and y components correctly. Magnitude-wise Vector B is also resolved correctly. But one additional thing to remember is the direction. For Vector B, the x-component will be -ve as Cos(120) = -0.5. Now the next step is to find the resultant x and y component due to the above two forces acting simultaneously, which will be Rx = (3 - 2.5) units = 0.5 units                                                          and Ry = 0 + 4.3 = 4.3 units. Hence the magnitude of resultant force will be R = sqrt(Rx^2 + Ry^2)                                                                          = sqrt(0.25 + 18.49)                                                                          = 4.329 units and the direction of this force will be making an angle ? with +ve x-axis given by       ? = arctan(Ry / Rx) = arctan(4.3 / 0.5) = 83.37deg. Hence we should apply a force equal in magnitude 4.329 units and opposite in direction to the above resultant force i.e., a force with 4.329 units and making an angle (180 + 83.37)deg = 263.37deg with +ve x-axis counter-clockwise. (Convert the angle with relative to vector B if you want to). Hope this helps you. (Convert the angle with relative to vector B if you want to). Hope this helps you.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.